Graphical Representations for One Quantitative Variable

Dotplots, stemplots, and histograms display one quantitative variable on a number line, ordered smallest to largest. A dotplot stacks one dot per observation; a stemplot splits each value into a stem and a leaf, so both keep every individual value readable. A histogram trades that detail for scale: it cuts the axis into equal-width bins and reports only how many observations fall in each, so its silhouette shows where values pile up and how far they spread. Bin width is the analyst's choice, and changing it changes the picture, so shape claims should rest on features that survive a change of bins.

The traps are two. First, reading a histogram like a bar chart: calling the tallest bar the largest value, counting bars to count data, or claiming a specific value is in the data because a bar covers it; a bar is a count over an interval, nothing finer. Second, naming skew from the pile instead of the tail: a distribution whose values crowd the low end with a thin reach toward high values is skewed right, because the tail, not the bump, gives the direction its name.